Question

If S is stress and Y is Young’s modulus of wire then energy stored in the wire per unit volume is?
(A) $\dfrac{{{S^2}}}{{2Y}}$
(B) $\dfrac{{2Y}}{{{S^2}}}$
(C) $\dfrac{S}{{2Y}}$
(D) $2{S^2}Y$

Answer 1

Hint Young's modulus is the mechanical property of material to resist compression or elongation with respect to its length. It is also denoted as Elastic modulus or Tensile modulus. Stress is the force acting per unit area of material.
Complete Step by Step Solution:
Energy stored per unit volume$= U = \dfrac{1}{2} \times stress \times strain$
$Strain = \dfrac{{Stress}}{Y}$
We are given that stress is S and Young's modulus is Y so substituting these expressions in the above equations gives us,
$U = \dfrac{{{S^2}}}{{2Y}}$

Correct answer is option A.

Additional Information:
As we have defined before stress is the force per unit area it can be of two types. Comprehensive stress and tensile stress. Comprehensive stress can be defined as the stress which causes decrease in length or unit area. The object under compressive stress becomes thicker and shorter. Tensile stress is the stress which caused increase in length or unit area. The object under tensile stress becomes thinner and longer.

Note:
An object under stress becomes deformed, the quantity that describes the deformation is called a strain. It is also classified as comprehensive and tensile strain. Comprehensive strain can be defined as the strain which causes change in length due to application of comprehensive strain and tensile strain can defined as the strain which caused change in length due to application of tensile strain.
Shear strain: The shear strain is defined as the angular distortion between two mutually perpendicular planes.
Volumetric strain: Volumetric strain is defined as the ratio of change in actual volume to the original volume.